Suppose that a certain college class contains 38 students. Of these, 23 are freshmen, 25 are English majors, and 11 are neither. A student is selected at random from the class.
(a) What is the probability that the student is both a freshman and an English major?
(b) Given that the student selected is a freshman, what is the probability that she is also an English major?
Write your responses as fractions. (If necessary, consult a list of formulas.)

Answer:

The answer to your problem is, A. The Allstars, with a mean of about 67.1 inches

Step-by-step explanation:

Allstars mean height:

= (73 + 62 + 60 + 63 + 72 + 65 + 69 + 68 + 71 + 66 + 70 + 67 + 60 + 70 + 71) / 15

= 1007 / 15

= 67.6 inches

Super Stars mean height:

= (66 + 68 + 62 + 63 + 47 + 64 + 65 + 50 + 60 + 64 + 65 + 65 + 58 + 60 + 55) / 15

= 912 / 15

= 60.2 inches

We can see that the Allstars team has a higher mean height than the Super Stars team, with an average of 67.6 inches compared to 60.2 inches. Therefore, the Allstars team typically has the tallest players

Thus the answer to your problem is, A. The Allstars, with a mean of about 67.1 inches

Answer:

$480

Step-by-step explanation:

From the above question, we are told that:

A saleswoman earns 60% commission on all that she sells. Last month she sold $800 worth of merchandise.

The amount of commission (In dollars) she earned last month is calculated as:

60% of $800

= 60/100 × $800

= $480

Therefore, the amount of commission shoe earned last month in dollars = $480

For

Example 1: Pair of lines are parallel.

Example 2: Pair of lines are perpendicular.

Example 3: Pair of lines are not parallel nor perpendicular.

Example 4: Pair of lines are perpendicular.

Example 5: Pair of lines are parallel.

Example 6: Pair of lines are parallel.

Example 7: Pair of lines are perpendicular.

Example 8:  Pair of lines are not parallel nor perpendicular.

What is the slope of the line in the slope-intercept form of the line?

If y = mx + c line is given then 'm' represents the slope of the line. If any pair of lines are given and if they have the same value of the slopes then we can say that the given pair of lines will be parallel in nature and if the slope of the one line is the negative inverse of the other line then we can say that the pair of lines are perpendicular to each other.

For example 1:

      y = 3x + 4 and y = 3x +7

     The slopes of both lines are equal hence, these pair of lines are parallel.

For example 2:

     y = -4x + 1 and 4y = x + 3

    Here, the slope of one line is the negative inverse of the other line hence this pair of lines are perpendicular to each other.

For example 3:

     y = 2x - 5 and y = 5x -5

   In this, the slopes are not equal so we can say that the graph of this pair of equations is not parallel nor perpendicular.

For example 4:

     y = -1/3x + 2 and y = 3x - 5

     Here, the slope of one line is the negative inverse of the other line hence this pair of lines are perpendicular to each other.

For example 5:

     y = 3/5x - 3 and 5y = 3x - 10

    The slopes of both lines are equal hence, these pair of lines are parallel.

For example 6:

     y = 4 and 4y = 6

     The slopes of both lines are equal hence, these pair of lines are parallel.

For example 7:

     y = 7x + 2 and x + 7y = 8

     Here, the slope of one line is the negative inverse of the other line hence this pair of lines are perpendicular to each other.

For example 8:

     y = 5/6x - 6 and x + 5y = 4

    In this, the slopes are not equal so we can say that the graph of this pair of equations is not parallel nor perpendicular.

Hence,

Example 1: Pair of lines are parallel.

Example 2: Pair of lines are perpendicular.

Example 3: Pair of lines are not parallel nor perpendicular.

Example 4: Pair of lines are perpendicular.

Example 5: Pair of lines are parallel.

Example 6: Pair of lines are parallel.

Example 7: Pair of lines are perpendicular.

Example 8:  Pair of lines are not parallel nor perpendicular.

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Answer:

4.1

Step-by-step explanation:

Answer:

Step-by-step explanation:

The mathematical translation of the statement:

\(\sqrt{121} = \sqrt{11 *11}\)

        \(= \sqrt{11^{2}}\)

        \(= (11^{2}) ^{\frac{1}{2} }\)

The indices will cancel each other out completely:

        \(= 11\)

OR:

\(\sqrt{121} = \sqrt{(-11)*(-11)}\)

        \(= \sqrt{(-11)^{2} }\)

        \(= [(-11)^{2}] ^{\frac{1}{2} }\)

        = -11

Let us assume a value, a for the other part of the base. thus, the length of the base of the triangle is d + a

Considering the right angle traingle containing y degrees,

opposite side = h

adjacent side = a

Tan# = opposite side/adjacent side

tan y = h/a

a = h/tany

Considering the right angle traingle containing x degrees,

opposite side = h

adjacent side = a + d

Tan# = opposite side/adjacent side

tan x = h/(a + d)

a + d = h/tanx

a = h/tanx - d

If we equate both a's, it becomes

h/tany = h/tanx - d

d = h/tanx - h/tany

The diagonal matrix that has these values would be:

16 0 0 0 0

0 -8.7 0 0 0

0 0 5.4 0 0

0 0 0 1.3 0

0 0 0 0 -6.9

This is the type of matrix that is written in the form where all of the entries that are outside the diagonal are zeros.

The diagonal is a line that divides a triangle into two halves. The diagonal here has all of the digits. Outside it are all zero elements.

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Answer:

C is the correct answer

Explanation:

Hope you have a great day!

According to the given statement The probability that the sum equals Erika's age in years is 2/12, which simplifies to 1/6.

To find the probability that the sum of the numbers equals Erika's age of 14, we need to consider all possible outcomes and calculate the favorable outcomes.
First, let's consider the possible outcomes for flipping the coin. Since the coin has sides labeled 10 and 20, there are 2 possibilities: getting a 10 or getting a 20.
Next, let's consider the possible outcomes for rolling the die. Since a standard die has numbers 1 to 6, there are 6 possibilities: rolling a 1, 2, 3, 4, 5, or 6.
To find the favorable outcomes, we need to determine the combinations that would result in a sum of 14.
If Erika gets a 10 on the coin flip, she would need to roll a 4 on the die to get a sum of 14 (10 + 4 = 14).
If Erika gets a 20 on the coin flip, she would need to roll an 8 on the die to get a sum of 14 (20 + 8 = 14).
So, there are 2 favorable outcomes out of the total possible outcomes of 2 (for the coin flip) multiplied by 6 (for the die roll), which gives us 12 possible outcomes.
Therefore, the probability that the sum equals Erika's age in years is 2/12, which simplifies to 1/6.

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If there is a positive correlation between x and y in the regression equation y = bx + a, then b > 0.

In the regression equation, y = bx + a, a positive correlation between x and y indicates that as the value of x increases, the value of y also increases, and vice versa. The correlation between these two variables is represented by the coefficient b in the equation.

A positive correlation means that b > 0, as a positive value for b will result in y increasing when x increases. On the other hand, if b < 0, it would indicate a negative correlation, meaning that y would decrease as x increases.

The constant term a in the equation represents the y-intercept or the value of y when x is equal to zero. It does not directly affect the correlation between x and y, so it can be either positive (a > 0) or negative (a < 0) depending on the specific data being analyzed. The value of a will only shift the position of the regression line on the graph, while the slope (b) determines the direction of the correlation between the variables.

In conclusion, if there is a positive correlation between x and y in the regression equation y = bx + a, then b > 0. The values of a > 0 or a < 0 are not directly related to the correlation between x and y.

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Answer: 76 degrees

Step-by-step explanation: All angles of a triange add up to 180. So, to find the missing angle we just have to add the other two angles and subtract the sum from 180.

1. 32 + 72 = 104.

2. 180- 104 = 76.

HOPE THIS HELPED YOU!

Answer:

32,29

Step-by-step explanation:

Answer:

(x,y) = (-3,-6)

Step-by-step explanation:

gm gn cgmcgmxgmgnx

The items matched in the left column to the items in the right column are

Ratio is the number representing a comparison between two named things or quantities.

1. total to fish

= 8 : 3

2. starfish to fish

= 5 : 3

3. starfish to total

= 5 : 8

4. fish to starfish

3 : 5

In conclusion, the ratio of the total to fish to starfish is 8 : 3 : 5

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Answer:

Negative

Step-by-step explanation:

When an even number of negatives are multiplied together, the product will be positive (because two negatives cancel out). When an odd number of negatives are multiplied together, the product will be negative.

In the given expression, there is also a singular (1) at the end, which we can ignore since anything multiplied by 1 is itself. The other numbers are all negative and there are 3 of them, and since 3 is an odd number, the product will be negative.

I hope this helps!

Answer:

The third choice

Step-by-step explanation:

Negative, because the product (–7)(–2) is positive, and the product (–5)(1) is negative and the product of a positive and a negative number is negative,

pls mark as brainliest hope you have a nice day!

The given equation is-

First, we move the independent term to the other side.

Now, we have to use the quadratic equation to find the solutions.-

Where, a = 1, b = -10, and c = 34.

Replacing these values in the formula, we have.

But, there's no square root of -36 because it's a negative. To solve this issue, we use complex numbers that way, we would have solutions.

The heat lost when the temperature difference is 15 degrees Celsius and thickness 0.2 cm is 5625 Calories.

The heat lost through the window is calculated by determining the value of constant in the joint variation.

h = ( kdA / t )

where;

k = ( ht ) / ( dA )

k = ( 9000 x 0.25 ) / ( 30 x 1500 )

k = 0.05

The heat lost when the temperature difference is 15 degrees Celsius and thickness 0.2 cm is calculated as;

h = ( kdA / t )

h = ( 0.05 x 15 x 1500 ) / ( 0.2 )

h = 5,625 calories

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Answer:

13

Step-by-step explanation:

7 + 6 = 13

Answer:

Step-by-step explanation:

If I found the mean, the answer would be:

3+ 4+4+4+5+6+7+23= 56

56/ 8 = 7

If I found the average value using the median, the answer would be 4.5.

In this set of data, the anomaly is 23 as it is much higher than the other numbers.

The median is more accurate because it find the more ‘central’ number and is not affected as greatly with anomalies whereas the mean is affected greatly with anomalies as it raises the value significantly.

Therefore, the median is better to work out the average in this set of data.

:)

Answer:

no solution

Step-by-step explanation:

the lines are parallel so they never touch, this means that there is no solution

Answer:

\(6 \frac{1}{12}\)

Step-by-step explanation:

1) Use Least Common Denominator or (LCD)

LCD = 12

2) Make the denominators the same as the LCD.

\(5 + \frac{1 times 4 }{3 times 4 } + \frac{3 times3}{4times 3}\)

3) Simplify. Denominators are now the same.

\(5 + \frac{4}{12} +\frac{9}{12}\)

4)  Join the denominators.

\(5+ \frac{4+9}{12}\)

5)  Simplify.

\(5+\frac{13}{12}\)

6) Convert 13/12 into a mixed number.

\(5+ 1 \frac{1}{12}\)

7)  Simplify.

\(6 \frac{1}{12}\)

Decimal Form: 6.083333

Permutation P-values should never be zero: calculating exact P-values when permutations are randomly drawn

This is a research paper whose authors are Belinda Phipson , Gordon K Smyth,

Abstract:

Conclusions:

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The approximate area of the window that is not cleaned by the wiper is:

240 - 100.5 ≈ 139.5 square inches. Answer: \boxed{139.5}.

What is circle?

A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center.

To solve this problem, we need to find the area of the trapezoid and subtract the area of the semicircle.

The area of a trapezoid is given by the formula:

A = (a + b)h/2

where a and b are the lengths of the parallel sides, and h is the height (the perpendicular distance between the parallel sides).

In this case, we have:

a = 24 inches (the top parallel side)

b = 16 inches (the bottom parallel side)

h = 12 inches (the height)

Using the formula, we get:

A = (24 + 16) x 12/2

A = 240 square inches

The area of a semicircle is given by the formula:

A = πr²/2

where r is the radius of the circle.

In this case, the radius is half of the length of the wiper, so we have:

r = 16/2 = 8 inches

Using the formula, we get:

A = π(8²)/2

A ≈ 100.5 square inches

Therefore, the approximate area of the window that is not cleaned by the wiper is:

240 - 100.5 ≈ 139.5 square inches. Answer: \boxed{139.5}.

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The response y(t) graphically, we can first plot the individual functions h(t) and x(t) on a graph, and then determine their convolution to obtain y(t). Let's go step by step:

Plotting h(t):

The function h(t) is defined as h(t) = [u(t-1) - u(t-4)].

The unit step function u(t-a) is 0 for t < a and 1 for t ≥ a. Based on this, we can plot h(t) as follows:

For t < 1, h(t) = [0 - 0] = 0

For 1 ≤ t < 4, h(t) = [1 - 0] = 1

For t ≥ 4, h(t) = [1 - 1] = 0

So, h(t) is 0 for t < 1 and t ≥ 4, and it jumps up to 1 between t = 1 and t = 4. Plotting h(t) on a graph will show a step function with a jump from 0 to 1 at t = 1.

Plotting x(t):

The function x(t) is defined as x(t) = t[u(t) - u(t-2)].

For t < 0, both u(t) and u(t-2) are 0, so x(t) = t(0 - 0) = 0.

For 0 ≤ t < 2, u(t) = 1 and u(t-2) = 0, so x(t) = t(1 - 0) = t.

For t ≥ 2, both u(t) and u(t-2) are 1, so x(t) = t(1 - 1) = 0.

So, x(t) is 0 for t < 0 and t ≥ 2, and it increases linearly from 0 to t for 0 ≤ t < 2. Plotting x(t) on a graph will show a line segment starting from the origin and increasing linearly with a slope of 1 until t = 2, after which it remains at 0.

Obtaining y(t):

To obtain y(t), we need to convolve h(t) and x(t). Convolution is an operation that involves integrating the product of two functions over their overlapping ranges.

In this case, the convolution integral can be simplified because h(t) is only non-zero between t = 1 and t = 4, and x(t) is only non-zero between t = 0 and t = 2.

The convolution y(t) = h(t) * x(t) can be written as:

y(t) = ∫[1,4] h(τ) x(t - τ) dτ

For t < 1 or t > 4, y(t) will be 0 because there is no overlap between h(t) and x(t).

For 1 ≤ t < 2, the convolution integral simplifies to:

y(t) = ∫[1,t+1] 1(0) dτ = 0

For 2 ≤ t < 4, the convolution integral simplifies to:

y(t) = ∫[t-2,2] 1(t - τ) dτ = ∫[t-2,2] (t - τ) dτ

Evaluating this integral, we get:

\(y(t) = 2t - t^2 - (t - 2)^2 / 2,\) for 2 ≤ t < 4

For t ≥ 4, y(t) will be 0 again.

Maximum value of y(t):

To find the value of t at which y(t) reaches its maximum value, we need to examine the expression for y(t) within the valid range 2 ≤ t < 4. We can graphically determine the maximum by plotting y(t) within this range and identifying the peak.

Plotting y(t) within the range 2 ≤ t < 4 will give you a curve that reaches a maximum at a certain value of t. By visually inspecting the graph, you can determine the specific value of t at which y(t) reaches its maximum.

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Answer:

? = 11.3

Step-by-step explanation:

This figure is a parallelogram which indicates that TW is parallel as well as congruent to UV, so;

TW ≅ UV

So if TW = 11.3 then, so would be UV

Hope this helps!

In the given scenario, the processor has a 32-bit address, and the main memory it is attached to has a capacity of 256 MB and can contain 65,536 pages.

A 32-bit address means that the processor can address 2³² (4,294,967,296) unique memory locations.

However, in this case, the main memory has a capacity of 256 MB, which is equivalent to 256 * 2²⁰bytes (268,435,456 bytes).

To determine the number of pages, we need to divide the memory size by the page size. Since the number of pages is given as 65,536, we can calculate the page size as 268,435,456 / 65,536 = 4,096 bytes.

Since the processor has a 32-bit address, it can address 2³² unique memory locations.

However, the main memory can only contain 65,536 pages, and each page is 4,096 bytes in size. T

his means that the processor can address a larger number of memory locations than the physical memory can accommodate. To access data beyond the capacity of the main memory, the processor would need to use virtual memory techniques such as paging or segmentation.

These techniques allow the processor to access data stored in secondary storage devices, such as hard drives, as if it were in main memory.

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The optimal values are: Units of chemical P, p = 144 units

Units of chemical R, r = 0 units

Maximum production of chemical Z, z = 24,480 units (rounded to the nearest whole unit)

To maximize the production of chemical Z subject to the budgetary constraint, we need to determine the optimal values for p (units of chemical P) and r (units of chemical R) that satisfy the budget constraint and maximize the production of Z.

Let's first set up the equations based on the given information:

Cost constraint equation:

400p + 1200r = 144000

Production equation:

z = 170p + 75r

We want to maximize z, so our objective function is z.

Now we can solve this problem using linear programming.

Step 1: Convert the problem into standard form.

Rewrite the cost constraint equation as an equality:

400p + 1200r = 144000

Step 2: Set up the objective function and constraints.

Objective function: Maximize z

Constraints:

400p + 1200r = 144000

z = 170p + 75r

Step 3: Solve the linear programming problem.

We can solve this problem using various methods, such as graphical method or simplex method. Here, we'll solve it using the simplex method.

The solution to the linear programming problem is as follows:

Units of chemical P, p = 144 (rounded to the nearest whole unit)

Units of chemical R, r = 0 (rounded to the nearest whole unit)

Maximum production of chemical Z, z = 170p + 75r = 170(144) + 75(0) = 24,480 units (rounded to the nearest whole unit)

Therefore, the optimal values are:

Units of chemical P, p = 144 units

Units of chemical R, r = 0 units

Maximum production of chemical Z, z = 24,480 units (rounded to the nearest whole unit)

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Answer:(-27,5)

Step-by-step explanation:

Answer:

Please send full question. What to find in this question?

Answer:

XY = 5.4cm,angle X = 30 degree,angle Y = 75 degree.it is your answer.

To find σg(X)^2, we need to calculate the variance of the function g(X) = 4X^2 + 2, where X is a random variable with a given density function. The density function is defined as f(x) = (3/2)(x + 1) for 0 ≤ x and 0 elsewhere. By calculating the variance of g(X), we can determine the value of σg(X)^2.

To calculate the variance of g(X), we first need to find the mean of g(X), denoted as E[g(X)]. For a continuous random variable, the mean is calculated as the integral of the function multiplied by the density function. In this case, we have:

E[g(X)] = ∫(4X^2 + 2) * f(x) dx

Substituting the given density function, we have:

E[g(X)] = ∫(4X^2 + 2) * (3/2)(X + 1) dx

After simplifying and evaluating the integral, we can find the value of E[g(X)].

Next, we calculate the variance of g(X), denoted as Var[g(X)]. The variance is calculated as the expectation of the squared difference between g(X) and its mean, E[g(X)]^2. In mathematical terms:

Var[g(X)] = E[(g(X) - E[g(X)])^2]

By substituting the values of g(X) and E[g(X)], we can evaluate this expression and find the value of Var[g(X)].

Finally, to find σg(X)^2, we take the square root of Var[g(X)], i.e., σg(X) = √Var[g(X)]. After calculating Var[g(X)], we can determine the value of σg(X) to three decimal places as needed.

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Answer:

True

This is so because the line is drawn from points on both sides of the line to be bisected, which are equidistant from the ends and the center of the line to be bisected line giving an angle of 90° at the intersection of both lines.

Step-by-step explanation:

The steps for constructing the bisector of a line segment includes the following

1) The compass is placed at one end of the line segment

2) The width of the compass is adjusted so as to be wider than half the length of the line segment

3) Arcs are now to be drawn above and below the line segment to be bisected

4) From the other end of the line to be bisected with the same compass width, draw arcs above and below the line segment to be bisected to intersect the previous arcs drawn above

5) With a straight edge draw a line through the intersection of the arcs to draw the bisector

The line so drawn is the perpendicular bisector because it is drawn from points on both sides of the bisected line equidistant from the ends and the center of the bisected line.